Hydrodynamic analysis of fin-fin interactions in two-manta-ray schooling in the vertical plane.

This study investigates the interaction of a two-manta-ray school using computational fluid dynamics (CFD) simulations. The baseline case consists of two in-phase swimming mantas arranged in a stacked configuration. Various vertical stacked and streamwise staggered configurations are studied by altering the locations of the top manta in the upstream and downstream directions. Additionally, phase differences between the two mantas are considered. Simulations are conducted using an in-house developed incompressible flow solver with an immersed boundary method. The results reveal that the follower will significantly benefit from the upstroke vortices (UVs) and downstroke vortices (DVs) depending on its streamwise separation. We find that placing the top manta 0.5 body length (BL) downstream of the bottom manta optimizes its utilization of UVs from the bottom manta, facilitating the formation of leading-edge vortices (LEVs) on the top manta's pectoral fins during the downstroke. This LEV strengthening mechanism, in turn, generates a forward suction force on the follower that results in a 72% higher cycle-averaged thrust than a solitary swimmer. This benefit harvested from UVs can be further improved by adjusting the phase of the top follower. By applying a phase difference of π/3 to the top manta, the follower not only benefits from the UVs of the bottom manta but also leverages the auxiliary vortices (AVs) during the upstroke, leading to stronger tip vortices and a more pronounced forward suction force. The newfound interaction observed in schooling studies offers significant insights that can aid in the development of robot formations inspired by manta rays.